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The Biggest Breakthroughs in Mathematics: 2025
2025 marked a historic year in mathematics. Researchers solved a major case of Hilbert’s ambitious sixth problem, proved a sweeping new theorem about hyperbolic surfaces, and settled the longstanding three-dimensional Kakeya conjecture.
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Subhash Khot: A Grand Vision for the Impossible
Subhash Khot’s bold conjecture is helping mathematicians explore the precise limits of computation.
In Noisy Equations, One Who Heard Music
Experts say Martin Hairer’s epic masterpiece in stochastic analysis “created a whole world.”
A Tenacious Explorer of Abstract Surfaces
Maryam Mirzakhani’s monumental work draws deep connections between topology, geometry and dynamical systems.
A Brazilian Wunderkind Who Calms Chaos
Artur Avila’s solutions to ubiquitous problems in chaos theory have earned him Brazil’s first Fields Medal.
Manjul Bhargava: The Musical, Magical Number Theorist
The search for artistic truth and beauty has led Manjul Bhargava to some of the most profound recent discoveries in number theory.
A ‘Rebel’ Without a Ph.D.
A conversation with the mathematical physicist Freeman Dyson on quantum electrodynamics, climate change and his latest pet project.